Economic Growth and Quality Adjusted HumanCapital Equation: Moderating Role of SocialCapabilities in AfricaTonuchi Emmanuel Joseph  ( tonuchijoseph@gmail.com )

Central Bank of Nigeria https://orcid.org/0000-0002-2010-0848Pauline Chimuru Obikaonu 

Central Bank of Nigeria

Research Article

Keywords: Africa, human capital, General Method of Moment (GMM), quality adjusted human capital,social capabilities

Posted Date: November 1st, 2021

DOI: https://doi.org/10.21203/rs.3.rs-1030633/v2

License: This work is licensed under a Creative Commons Attribution 4.0 International License.  Read Full License

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Economic Growth and Quality Adjusted Human Capital Equation: Moderating Role of

Social Capabilities in Africa

Tonuchi E Joseph1,2, Obikaonu C. Pauline1

1. Central Bank of Nigeria, Abuja

2. Corresponding author: tonuchijoseph@gmail.com

Abstract

The role of human capital on economic growth across countries has over time garnered lots of

discussion in economic literature. This is fundamental, given that the actual determinant of the

difference in income per capita across countries or why some countries are growing faster than

other countries has remained an unresolved issue. This study provides a different insight into

the nexus between human capital and economic growth by accounting for the role of social

capabilities in a panel framework. Specifically, the study covers 40 African countries between

1998-2019, where the General Method of Moment (GMM) was employed to estimate the

model. Specifically, it was discovered that without improved legal institutions and better

economic opportunities, human capital impact on the growth of income per capita across

countries is insignificant though positive. The study concludes that the effectiveness of

knowledge accumulation and adoption of technology in a country is hinged on the availability

of an enhanced legal, social, and economic environment.

Keywords: Africa, human capital, General Method of Moment (GMM), quality-adjusted

human capital, social capabilities

JEL CODE: A3, D83, E24, F63, I2

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1. Introduction

What determines the differences in cross-country income and long-run economic growth rate

across countries remains a controversial and highly debated topic among economists (Adler et

al., 2017). The global economy has witnessed tremendous growth in output per capita in the

last four decades, with world average growth rate at 4.3 percent between 1987 and 2015 (United

Nation Report, 2018). Despite the outstanding growth rate witnessed in the past three decades

championed by the East Asian countries (China, India & Asian tigers), the growth rate in the

last decades has been met with lots of economic crises and global negative shocks. This global

economic crisis and shocks include the global financial crisis of 2008 to 2010 championed by

the US, the European debt-crisis of 2010 to 2012 championed by Argentina, the global

commodity price fluctuation or falls championed by oil-producing countries including Nigeria

(2014-2016), and more recently the global negative output shock induced by Covid 19

pandemic (Joseph, 2020).

In the past three decades, empirical evidence has revealed that human capital accumulation,

physical capital stock, technological adoption (machine and equipment), institutional

framework, quality, and quantity of labour force are among the leading drivers of the difference

in cross country income (Obialor, 2017; Izushi & Huggins, 2004; Barro, 1998, Orogwu et al,

2021). Data from International Monetary Fund (2017) revealed that machinery and intellectual

properties (human capital and technology advancement) are the leading drivers of growth in

most developed countries, including the US, EU, Japan, and South Korea. Although, data

revealed that China's outstanding economic growth, which has lasted for decades, cannot be

attributed to intellectual properties but rather accumulation and stock of physical and human

capital (Tonuchi & Onyebuchi, 2019). Izushi and Huggins (2004) noted that China is enjoying

technological diffusion partly necessitated by trade policies from the West.

Economic growth theories postulate that the determinant of economic growth across countries

is the differences in technology adoption and human capital accumulation. Specifically, the

endogenous growth model states that technological advancement is directly related to

investment in human capital. Similarly, the human capital theory postulates that the higher the

quantity of schooling society the higher the economic growth (state of the economy). However,

available evidence revealed that the increased global quantity of education or schooling had

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not yielded much impact on economic growth, especially in developing countries (IMF, 2017).

Bobetko, Draženović & Funda (2017) noted that rising school enrollment worldwide did not

yield much equitable income distribution, economic growth, and development, especially in

Africa. Evidence revealed that the global average of school enrollment has risen by 240 percent

between 1960 and 2015, while global income per capita has only grown by 19.44 percent within

the same period (World Bank, 2016). The missing link here is the fact that a mere rise in school

enrollment does not guarantee quality education, improved economic opportunities, and a

quality workforce. It borders on the question of whether the workforce (for example university

graduates) is competent and employable, given that available evidence shows that cognitive

skills and institutional quality (level of economic opportunities, democratic system, and quality

education) are major determinants of how effective human capital is in driving economic

growth (Ali et al., 2018; Hanushek, 2013; Joseph et al, 2021). This lack of emphasis on the role

of institutions and quality of education in the most empirical literature on growth as well as

policy framework including the popular MDGs programme brings to limelight the huge policy

lacuna in most growth and developmental policies across the globe.

To this end, this study aims to determine the role of social capabilities in the nexus between

human capital and the difference in cross-country growth rate. The rest of the paper is

structured in the form of a literature review, methodology, analysis, and conclusion.

2. Literature Review

2.1 Theoretical Evidence

The role of human capital and recently human capital interaction with social capability (role of

the institution and legal framework) in driving economic growth has received substantial

theoretical and empirical discussion since the work of Schultz (1961) and Becker (1962).

Solow (1956) growth model arguably appears to be the most potent first theoretical foundation

explaining differences in cross-country per capita income and factors that account for the long-

run economic growth of a country (Ali et al., 2018; Izushi & Huggins, 2004).

In an attempt to explain the factors responsible for the long-run economic growth and

differences in cross country income per capita; Solow relies on four major variables thus:

Y = F(K, AL) …………………………………………………………..(1)

where; Y = output, K = capital stock and L = labour force and A = Labour

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Effectiveness. By employing Cobb-Douglas production function, equation (1) can be re-written

as;

Y= 𝐾𝐾𝛼𝛼𝐴𝐴𝐴𝐴1−𝛼𝛼, 0 < α <1 ………………………………………….………… (2)

To see this, we can write the output per effective labour as a function of the effectiveness of

capital per labour by multiplying 1/AL all through as seen in equation (3) below.

y = 𝑘𝑘𝛼𝛼 = f (k) ……………………………………………………………… . (3)

Such that, f ’> 0 and f ’’ < 0. Equation three entails that labour productivity can only be

achieved through more capital deepening, that is, increasing capital intensity (Izushi &

Huggins, 2004). Overall, the assumption of diminishing returns to capital entails that output

per effective worker does not increase indefinitely with an increase in capital, so long as

individuals save a constant fraction of their income (s), and depreciation occurs on capital

investment (𝛿𝛿). Where ‘n’ represents population growth and ‘g’ represent knowledge growth

rate, such that the rate of increase in capital (k) can be written as;

∆𝑘𝑘∆𝑡𝑡 = 𝑠𝑠𝑠𝑠(𝑘𝑘) − (𝑛𝑛 + 𝑔𝑔 + 𝛿𝛿)𝑘𝑘 …………………………………………. (4)

when ∆𝑘𝑘∆𝑡𝑡 = 0; 𝑠𝑠𝑠𝑠(𝑘𝑘) = (𝑛𝑛 + 𝑔𝑔 + 𝛿𝛿)𝑘𝑘 …………………………..…….. (5)

Or, 𝑠𝑠(𝑘𝑘) = (𝑛𝑛 + 𝑔𝑔 + 𝛿𝛿)𝑘𝑘 𝑠𝑠� …………………………………………… (6)

Equations (5) and (6) are the key equation of the Solow neoclassical model. The equation states

that the derivative of 𝑘𝑘 is the difference between the per unit of actual investment per labour

and the amount of investment that must be done to keep capital per unit of effective labour (k)

at that point (Romer, 2012). Solow concludes that regardless of where the economy starts, the

economy will converge where output per worker (y) will be growing at the rate g. Meaning

that knowledge or technological progress is the only source of growth in such an economy

(Ludema, 2014; Barro, 1998).

However, following the work of Mankiw et al. (1992), equation (1) can be rewritten by

assuming that technology progress (A) does not enter the model multiplicatively to capture the

current state of technological knowledge as given in equation (7);

Y = F (A, K, L) ………………………………………………………… (7)

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Thus, if we assume that productivity increases over time at a constant rate g, equation (2), can

be rewritten as;

Y = 𝐴𝐴0𝑒𝑒𝑔𝑔𝑡𝑡𝐾𝐾𝛼𝛼𝐴𝐴1−𝛼𝛼, where A = 𝐴𝐴0𝑒𝑒𝑔𝑔𝑡𝑡 ………………………..…. (8)

If we substitute equation (8) with the knowledge of equation into Cobb-Douglas production

function, we have the estimated Solow Growth model as given below;

Ln �𝑌𝑌𝐿𝐿� = ln𝐴𝐴(0) + 𝑔𝑔𝑔𝑔 + 𝛼𝛼1−𝛼𝛼 ln(𝑠𝑠) − 𝛼𝛼1−𝛼𝛼 ln (𝑛𝑛 + 𝑔𝑔 + 𝛿𝛿) …………… (9)

The central hypothesis of the Solow growth model is that the steady-state level of per capita

income is determined by initial stock of technology A(0), savings rate (s) equal ratio of

investment to GDP, labour force growth rate (n), depreciation (𝛿𝛿), capital share (𝛼𝛼) (and

technology parameter (Mankiw et al., 1992). This means that if labour and capital stock is

growing at the same rate output per worker will surely grow so long technical progress (A) is

higher than zero.

The traditional Solow model has been severely criticized, the most prominent criticism of the

Solow model is the inability of the model to explain the causes of technological progress. While

the model was able to explain that the source of economic growth across countries can be

attributed to technological progress, the model did not explain how technological progress is

attained (Ali et al., 2018; Holden & Biddle, 2016). As Sapkota (2014) argued, Solow set the

rate of technological progress at ‘g’ but fails to explain how it relates to other variables in the

models. In response, to the above Criticism, Mankiw, Romer & Weil (1992) in the modified

version of Solow model noted that technological progress originates from knowledge generated

from learning institutions and Research and Development (R&D) base (universities, Non-

Government Organisations, and Public and private research institutes) that operate outside the

domain of the economic system.

However, technological progress cannot be ruled away from economic agents' economic

decisions like the capital accumulation decision. Economic agents are always looking for an

opportunity to exploit and produce a new idea in order to maximise profit. Thus knowledge-

creating process should be incorporated into the growth model. This implies that technological

progress should be endogenized in the growth equation (Holden & Biddle, 2016). Thus, Solow

growth model has been modified by Mankiw et al. (1992) to incorporate human capital as a

factor of production where average secondary school attainment has been a popular variable

5

used along others to capture human capital in the production function. The modified augmented

Solow Growth model is given as;

Y= 𝐾𝐾𝛼𝛼𝐻𝐻𝛽𝛽𝐴𝐴𝐴𝐴1−𝛼𝛼−𝛽𝛽, 0 < α + β <1 …………………………………………. (10)

where; H is the stock of human capital, the β share of human capital in the country GDP other

variables remain as defined earlier. As in the traditional Solow model, α + β <1 is based on the

assumption of decreasing returns to scale, contrary to endogenous growth theory. Following

the assumption Mankiw et al. (1992), let sk equal share of output invested in physical capital

and sh equals the share of output invested in human capital. Such that, the growth of income

per capita will be given as;

∆𝑘𝑘∆𝑡𝑡 = 𝑠𝑠𝑘𝑘𝑠𝑠(𝑘𝑘) − (𝑛𝑛 + 𝑔𝑔 + 𝛿𝛿)𝑘𝑘 = 𝑠𝑠𝑘𝑘(𝑘𝑘𝛼𝛼)ℎ𝛽𝛽 − (𝑛𝑛 + 𝑔𝑔 + 𝛿𝛿)𝑘𝑘 …………… (11a)

∆ℎ∆𝑡𝑡 = 𝑠𝑠ℎ𝑠𝑠(𝑘𝑘) − (𝑛𝑛 + 𝑔𝑔 + 𝛿𝛿)ℎ = 𝑠𝑠ℎ(𝑘𝑘𝛼𝛼)ℎ𝛽𝛽 − (𝑛𝑛 + 𝑔𝑔 + 𝛿𝛿)ℎ …………… (11b)

where; h = H/AL and others remain as earlier defined. Substituting (11a) and (11b) into (10),

we have;

Ln�𝑌𝑌𝐿𝐿� = ln𝐴𝐴(0) + 𝑔𝑔𝑔𝑔 − 𝛼𝛼+𝛽𝛽1−𝛼𝛼−𝛽𝛽 ln(𝑛𝑛 + 𝑔𝑔 + 𝛿𝛿) +

𝛼𝛼1−𝛼𝛼−𝛽𝛽 ln(𝑠𝑠𝑘𝑘) + 𝛽𝛽1−𝛼𝛼−𝛽𝛽 ln(𝑠𝑠ℎ) …. (12)

Following equation (12) above, theoretically, capital share (𝛼𝛼) =1/3, where the elasticity of per

capita output with respect to s and (𝑛𝑛 + 𝑔𝑔 + 𝛿𝛿) equal to 0.5 and -0.5, any deviation from this

point is assumed not significant or accurate modeling (Mankiw, et al.,1992).

One major theoretical issue in human capital theory is whether every aspect of investment in

education (teaching, training, and learning) should be considered human capital development

regardless of whether it increases the individual's productivity. Another challenge is the

inability of the theory to explain the high unemployment witnessed currently all over the world

except a few developed countries. Of course, the recent trade war among leading developed

countries like USA, Europe, and China is partly the quest to solve unemployment in their

respective country despite the high stock of human capital and technological advancement. In

developing countries, especially in sub-Saharan African countries like Nigeria. There seems to

be an increase in average secondary and tertiary school attainment, yet the unemployment level

is still rising, and economic growth is still performing poorly, among other indicators

contradicting the human capital theory.

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2.2 Empirical Evidence.

Several empirical works have investigated the impact of human capital on cross-country

income differences. In summary, human capital theory attributes knowledge as the most potent

driver of economic growth across countries (Ali et al., 2018; Ludema, 2014; Barro, 1998;

Shultz, 1961).

One of the earliest literature to investigate human capital and economic growth across countries

is Barro (1991). Barro employed a series of human capital variables with emphasis on the

quantity of education and growth rate per capita income. Using OLS, Barro (1991) found that

school enrolment rate is positively related to the growth rate of income per capita for a given

level of initial per capita income using data from 100 countries. Barro (1998) later re-examined

the relationship between human capital and economic growth using the same data set but made

a series of modifications to the data used and assumption. For instance, Barro disaggregates

the data for school enrollment to males and females to check whether gender influences the

extent the human capital impacts economic growth. The result revealed that male school

attainment at level has a significant positive impact on the growth rate of income per capita

across countries while female school attainment does not have any significant impact.

In response to criticism of using school enrolment as measure of human capital that ignores

quality, in 1998, Barro further examined whether school quality has any significant impact on

how human capital influences the cross-country economic growth rate. He employed students'

scores in science to achieve this, which positively impacted the human-economic growth rate

nexus. Mankiw et al. (1992) investigated both Solow growth model and the augmented Solow

model, where they introduce human capital variables in the model using panel data. They

model the growth rate of income per capita as a function of income per capita at level,

population growth rate, real investment ratio, average secondary school attainment as human

capital variables, and other variables. They argued that the addition of the human capital

variable in the model was able to explain the disparity in the growth rate of income per capita

among different countries of the world. They argue that there will be convergence in the long

run as more developing countries invest more in human capital accumulation. These countries

will be able to successfully imitate the technological advancement of the developed countries.

They used the lag one of the per capita growth rate to determine Solow conditional

convergence.

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Benhabib & Spiegel (1994) investigated the applicability of the Mankiw et al. (1992)

augmented Solow model. The authors first duplicated the Mankiw model using Cobb-Douglass

production function where human capital captured as years of secondary school enrolment was

used as input in the production function. It was revealed from the findings that human capital

used as part of input in the production function does not have a significant positive impact on

the difference in income per capital across countries, contrary to the significant positive impact

found by Mankiw et al. (1992). In a second model, the researcher investigated the endogenous

model that argued that human capital does not directly enter the growth equation but through

innovation and technological diffusion. The authors modeled technological diffusion and

innovation using total factor productivity as a function of human capital. It was discovered that

human capital has a significant positive relationship with technological diffusion and

innovation based on the data set used to estimate the relationship. Therefore, the authors

concluded that human capital surely impacts the difference in cross-country income through

technological diffusion and innovation and not directly on the income as treated by Mankiw et

al. (1992).

Similarly, Caselli et al. (1996), following Mankiw et al. (1992) estimated the growth rate

income per capita determinant across the country using cross-country panel data in the

framework of generalized method of moment (GMM). The authors like Islam (1995) criticize

the methodological approach employed by Mankiw et al. (1992) on the ground that one at least

of the explanatory variables might be endogenous, leading to a wrong prediction of

convergence between developing countries and developed countries in the long run. In dealing

with endogeneity and estimation bias issues, the author recommended the use of GMM as the

appropriate estimation technique. They argue that time-invariant of country-specific effect and

the lagged dependent variables, OLS, and fixed-effect (within the group) might lead to upward

bias and possibly generate an upward correlation between the lagged dependent variables and

the country-specific effect. This will make OLS (Mankiw et al., 1992) bias and inconsistent.

Using the General method of moment (GMM) as suggested to estimate the model, they found

that real income per capita converges to a steady-state in the long run by at least 10 percent per

annum.

A critic of Caselli et al.. (1996) methodological approach is that of Bond, Hoeffler, & Temple

(2001) using cross-country panel data. The authors criticize Caselli et al. (1996) first difference

estimation in terms of precision and bias. They argue that the first difference estimator has a

large finite downward bias, basically because of the small sample period. The view is that

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Caselli et al.. (1996) first difference estimation in GMM framework might perform poorly due

to the weak instrument. As such, Bond et al. (2001) recommended the application of system

GMM instead of the first difference GMM as applied by Caselli et al.. Since system GMM has

the original equation, it improves efficiency and reduces the level of finite sample bias.

Sunde & Vischer (2015) further examined the factor responsible for the weak empirical effect

of human capital on growth rate per capita among most cross countries literature. They argued

on the issues with the neoclassical growth model, which ignores most of the important variables

through which human capital impact the economic growth of a country affects the models. The

authors employed cross-country panel data for 80 countries using three different data set for

capturing average years of schooling (channels through which human capital impacts growth

rate per capita). Using school enrolment average, international student scores, and mean years

of schooling measure human capital on economic growth. They argued that human capital,

when controlled for measurement error and heterogeneity, has a significant impact on GDP

growth across countries.

Recent, literature tends to account for social capabilities interaction with human capital in

explaining the existing nexus between human capital and economic growth. As argued by Ali

et al. (2018), the social capabilities within a country impact the growth process by influencing

the quality and effectiveness of the normal production factors, including human capital. As

noted by the author, social capabilities encompass formalized institutions' role, like rule of law,

court system, political liberation, democracy prevalence in enhancing human capital. This

prompted Ali et al. (2018), to argue that institutional factors should be incorporated in the

growth equation, it the exact influence of human capital on the growth rate across countries

will be extracted. Several measures have been used in literature to measure the influence of

social capability as it interacts with human capital and economic growth across country. It was

revealed that human capital significantly impacts income per capita growth rate when there are

better opportunities and high-quality legal institutions are available.

3. METHODOLOGY

3.1 Data and Sources

All data are either sourced from World Bank Development Indicators (WDI), Penn World

databank, v8.0, and Economic Freedom Data set of Fraser Institute1. The most common human

1 https://www.fraserinstitute.org/economic-freedom/

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capital proxy used in literature is secondary and primary school enrolment (Barro, 1998) data

available in Barro & Lee (2011). However, given the recent argument in literature that human

capital proxy based on school enrollment does not provide a good description of a country

educational system, the researcher employed a robust human capital index that captured years

of schooling, quality of education, and returns on education at Penn World database as a proxy

for human capital. Social capabilities indices will be sourced from the economic freedom data

bank. The three leading social capability indices include political freedom (captured by

democracy index), economic opportunities (captured by property and legal right), and freedom

to trade locally and internationally (captured by trade openness). The index score is between 0

&10 where 10 represents the highest level of freedom and 0 represents the lowest level of

freedom. For instance, a well-established democratic setting improves the legal institution of

a country through effective check and balances, reduces abuse of power, reduce corruption and

increase investment since the investor believes in government accountability. Democracy is

said to guarantee more equitable redistribution of income which is capable of reducing unrest,

violence, and social revolution, which have a negative relationship with investment cum

economic growth. Again, the legal and property right is also a component of the economic

freedom index that is made up of factors relating to the prevailing quality of legal institutions.

3.2 Model Specification

To understand how human capital impacts the output per capital across the country. We model

the equation following the work of Ali et al. (2018), and Benhabib & Spiegel (1994) by

employing a simple Cobb-Douglas production function in an augmented Solow model

framework as in equation (13), 𝑌𝑌𝑖𝑖,𝑡𝑡= 𝐴𝐴𝑖𝑖,𝑡𝑡𝐾𝐾𝑖𝑖,𝑡𝑡𝛼𝛼 𝐴𝐴𝑖𝑖,𝑡𝑡𝜂𝜂 𝐻𝐻𝑖𝑖,𝑡𝑡𝜃𝜃 𝜀𝜀𝑖𝑖,𝑡𝑡 ………………………………………………. (13)

where; Y represents the growth rate of GDP per capita at current PPP, L represents labour force

employed at age 15 and above (Cohen & Soto, 2007), K represents the stock of physical capital

at current PPP, A represents the technological progress, and H is the vector of human capital

variables and 𝜀𝜀 is the error term. Taking the log of equation (13) as in equation (14). 𝑙𝑙𝑛𝑛𝑙𝑙𝑖𝑖,𝑡𝑡 − 𝑙𝑙𝑛𝑛𝑙𝑙0 = (𝑙𝑙𝑛𝑛𝐴𝐴𝑖𝑖,𝑡𝑡 − 𝑙𝑙𝑛𝑛𝐴𝐴0) + 𝛼𝛼(𝑙𝑙𝑛𝑛𝐾𝐾𝑖𝑖,𝑡𝑡 − 𝑙𝑙𝑛𝑛𝐾𝐾0) + 𝜂𝜂(𝑙𝑙𝑛𝑛𝐴𝐴𝑖𝑖,𝑡𝑡 − 𝑙𝑙𝑛𝑛𝐴𝐴0) + 𝜃𝜃(𝑙𝑙𝑛𝑛𝐻𝐻𝑖𝑖,𝑡𝑡 − 𝑙𝑙𝑛𝑛𝐻𝐻0) + (𝜀𝜀𝑖𝑖,𝑡𝑡− 𝑙𝑙𝑛𝑛𝜀𝜀0) ……… ……………………… (14)

Equation (14) can be written in its difference form as;

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𝛥𝛥𝑙𝑙𝑛𝑛𝑙𝑙𝑖𝑖,𝑡𝑡 = 𝛥𝛥𝑙𝑙𝑛𝑛𝐴𝐴𝑖𝑖,𝑡𝑡 + 𝛼𝛼𝛥𝛥𝑙𝑙𝑛𝑛𝐾𝐾𝑖𝑖,𝑡𝑡 + 𝜂𝜂𝛥𝛥𝑙𝑙𝑛𝑛𝐴𝐴𝑖𝑖,𝑡𝑡 + 𝜃𝜃𝛥𝛥𝑙𝑙𝑛𝑛𝐻𝐻𝑖𝑖,𝑡𝑡 + 𝛥𝛥𝜀𝜀𝑖𝑖,𝑡𝑡 ……… (15)

Most empirical literature reviewed often employed lagged dependent variables among the

covariate to account for simultaneity bias, mostly resulting from the unobserved effect from

experience and qualification in H. It is also used to check for Solow conditional convergence

(Mankiw et al., 1992). One lagged is used since, the unobserved is mostly reflected in output

after a time lag (Ali et al., 2018), as such, one period of lag will be used in the covariates.

Equation (15) can be modified to introduce the human capital in level form, incorporating this

and the issue of simultaneity, equation (15) can be re-written as; 𝛥𝛥𝑙𝑙𝑛𝑛𝑙𝑙𝑖𝑖,𝑡𝑡 = 𝛽𝛽0 + 𝛽𝛽1𝑙𝑙𝑛𝑛𝐴𝐴𝑖𝑖,𝑡𝑡 + 𝛼𝛼𝛥𝛥𝑙𝑙𝑛𝑛𝐾𝐾𝑖𝑖,𝑡𝑡 + 𝜂𝜂𝛥𝛥𝑙𝑙𝑛𝑛𝐴𝐴𝑖𝑖,𝑡𝑡 + 𝜃𝜃𝛥𝛥𝑙𝑙𝑛𝑛𝐻𝐻𝑖𝑖,𝑡𝑡 + 𝛽𝛽2𝑙𝑙𝑛𝑛𝐻𝐻𝑖𝑖,𝑡𝑡 + 𝛽𝛽3𝑙𝑙𝑛𝑛𝑙𝑙𝑖𝑖,𝑡𝑡−1 + 𝜆𝜆𝑖𝑖 + 𝛥𝛥𝜀𝜀𝑖𝑖,𝑡𝑡 ……… (16)

where 𝜆𝜆𝑖𝑖 capture the country-specific characteristics. To see if accounting for social

capabilities changes the Solow conditional convergence and the nexus between human capital

and economic growth, equation (16) will be modified to include a number of institutional and

social capabilities variables. 𝛥𝛥𝑙𝑙𝑛𝑛𝑙𝑙𝑖𝑖,𝑡𝑡 = 𝛽𝛽0 + 𝛽𝛽1𝑙𝑙𝑛𝑛𝐴𝐴𝑖𝑖,𝑡𝑡 + 𝛼𝛼𝛥𝛥𝑙𝑙𝑛𝑛𝐾𝐾𝑖𝑖,𝑡𝑡 + 𝜂𝜂𝛥𝛥𝑙𝑙𝑛𝑛𝐴𝐴𝑖𝑖,𝑡𝑡 + 𝜃𝜃𝛥𝛥𝑙𝑙𝑛𝑛𝐻𝐻𝑖𝑖,𝑡𝑡 + 𝛽𝛽2𝑙𝑙𝑛𝑛𝐻𝐻𝑖𝑖,𝑡𝑡 + 𝛽𝛽2𝑙𝑙𝑛𝑛𝑙𝑙𝑖𝑖,𝑡𝑡−1 + 𝛽𝛽4𝑙𝑙𝑛𝑛𝑙𝑙𝑙𝑙𝑖𝑖,𝑡𝑡 + 𝛽𝛽5𝑙𝑙𝑛𝑛𝑙𝑙𝑙𝑙𝑙𝑙𝑖𝑖,𝑡𝑡 + 𝛽𝛽6𝑙𝑙𝑛𝑛𝐴𝐴𝑙𝑙𝑖𝑖,𝑡𝑡 + 𝜆𝜆𝑖𝑖 + 𝛥𝛥𝜀𝜀𝑖𝑖,𝑡𝑡…… (17)

TO represents trade openness, DDI represents democracy index, and LP represents the

prevailing legal and property rights. It is expected that the three social capabilities variables

shall have a positive relationship with economic growth holding other determinants constant

and will improve the rate of conversion and technological diffusion.

We further modified equation (17) by interacting human capital with the social capabilities

variables to see whether the relationship will still hold and be significant as in equation (18).

The argument is that a well-functioning institution and legal environment provides more

political and economic opportunities to the citizens thereby reinforcing investment knowledge

accumulation. 𝛥𝛥𝑙𝑙𝑛𝑛𝑙𝑙𝑖𝑖,𝑡𝑡 = 𝛽𝛽0 + 𝛽𝛽1𝑙𝑙𝑛𝑛𝐴𝐴𝑖𝑖,𝑡𝑡 + 𝛼𝛼𝛥𝛥𝑙𝑙𝑛𝑛𝐾𝐾𝑖𝑖,𝑡𝑡 + 𝜂𝜂𝛥𝛥𝑙𝑙𝑛𝑛𝐴𝐴𝑖𝑖,𝑡𝑡 + 𝜃𝜃𝛥𝛥𝑙𝑙𝑛𝑛𝐻𝐻𝑖𝑖,𝑡𝑡 + 𝛽𝛽2𝑙𝑙𝑛𝑛𝐻𝐻𝑖𝑖,𝑡𝑡 + 𝛽𝛽2𝑙𝑙𝑛𝑛𝑙𝑙𝑖𝑖,𝑡𝑡−1 + 𝛽𝛽4𝑙𝑙𝑛𝑛𝑙𝑙𝑙𝑙𝑖𝑖,𝑡𝑡 + 𝛽𝛽5𝑙𝑙𝑛𝑛𝑙𝑙𝑙𝑙𝑙𝑙𝑖𝑖,𝑡𝑡 + 𝛽𝛽6𝑙𝑙𝑛𝑛𝐴𝐴𝑙𝑙𝑖𝑖,𝑡𝑡 + 𝛽𝛽7𝑙𝑙𝑛𝑛𝑙𝑙𝑙𝑙𝑖𝑖,𝑡𝑡 ∗ 𝑙𝑙𝑛𝑛𝐻𝐻𝑖𝑖,𝑡𝑡 +

𝛽𝛽8𝑙𝑙𝑛𝑛𝑙𝑙𝑙𝑙𝑙𝑙𝑖𝑖,𝑡𝑡 ∗ 𝑙𝑙𝑛𝑛𝐻𝐻𝑖𝑖,𝑡𝑡 + 𝛽𝛽9𝑙𝑙𝑛𝑛𝐴𝐴𝑙𝑙𝑖𝑖,𝑡𝑡 ∗ 𝑙𝑙𝑛𝑛𝐻𝐻𝑖𝑖,𝑡𝑡 + 𝜆𝜆𝑖𝑖 + 𝛥𝛥𝜀𝜀𝑖𝑖,𝑡𝑡…… (18)

11

where 𝛽𝛽7 to 𝛽𝛽9 are the parameter estimate of the moderating factors between human capital -

economic growth nexus. The parameter estimate of the moderating factors is expected to

positively correlate with economic growth since the above factors theoretically enhance human

capital capabilities and productivity.

3.3 Estimation Procedure

The panel data will be subjected to a stationarity test to ensure the data are free from unit root.

In a panel framework, the stationarity test developed over time can generally be grouped into

the first generation that imposes the restriction that the time series in the panel data has cross-

sectional independence. Such an assumption is necessary to satisfy Lindberg-Levy central limit

theorem and easily obtain asymptotic normal distribution test (Im, Pesaran and Shin test, 2003;

Mandala & Wu, 2000; Hadri, 2000). While the second generation tried to overcome the

assumption made by the first generation to allow for the situation where the time series in the

panel data have cross-sectional dependence (Bai & Ng, 2004; Moon and Perron, 2004). This

article adopted the first-generation panel unit root test as the study maintains the assumption

of independent cross-sectional correlation.

To estimate the models, this study shall rely on General Methods of Moments (GMM). Most

growth models explained the impact of human capital on the differences in income per capita

across countries using panel OLS (Barro, 1991), panel fixed and random effect (Islam, 1995),

First difference GMM (Caselli et al., 1996). Fixed effect, for instance, allow the estimation of

the unobserved country-specific effect 𝜆𝜆𝑖𝑖 as in equations (16) to (18), this is based on the

several advantages it has – reduces measurement errors among others.

As compared to fixed effect and random effect, GMM offered more robust estimation

advantages over the other estimation techniques in panel data estimation. The argument is that

time-invariant of country-specific effect and the lagged dependent variable, OLS, and Fixed-

effect (within the group) might lead to an upward bias. This will make OLS (Mankiw et al.,

1992) and fixed effect (Islam, 1995) bias and inconsistent. Also, it enables the correction of

endogeneity common in growth equation by adding lagged of the independent variables as

instruments in the equation. In the study following Dansasi (2013), Bond et al. (2001)

employed system GMM to investigate the relationship since it improves efficiency and reduces

the level of finite sample bias. The first difference GMM will not be used considering the

argument of Bond et al. (2001), who noted that first difference estimation in GMM framework

might perform poorly due to the weak instrument.

12

The GMM is an econometric approach that combines observed time series alongside

information in the population moment conditions to generate parameter estimate of the

economic relationship. It relies on population information on the first four moment, mean,

variance, skewness and kurtosis. To see this clearly, in a dynamic framework, the growth

equation can be written as follow in (19); 𝑙𝑙𝑖𝑖𝑡𝑡 = α+ 𝛾𝛾1𝑙𝑙𝑛𝑛𝑙𝑙𝑖𝑖𝑡𝑡−1 + 𝛽𝛽′[𝑋𝑋]𝑖𝑖𝑡𝑡 + 𝜆𝜆𝑖𝑖 + 𝜀𝜀𝑖𝑖𝑡𝑡 …………………………… (19)

where; 𝑙𝑙𝑖𝑖𝑡𝑡 is the output per capita as the dependent variable and 𝑙𝑙𝑛𝑛𝑙𝑙𝑖𝑖𝑡𝑡−1 is the lagged explained

variable and 𝑋𝑋𝑖𝑖𝑡𝑡 is the vector of independent variables including the human capital and the

social capability (moderating variables), 𝜀𝜀𝑖𝑖𝑡𝑡 error term that has constant means, E [𝜀𝜀𝑖𝑖𝑡𝑡] = 0.

other variables remain as defined earlier. And i = 1, …... N., and t = 2, ……, T. also, [𝜆𝜆𝑖𝑖 + 𝜀𝜀𝑖𝑖𝑡𝑡] is the standard error component. We assume that, E [𝜆𝜆𝑖𝑖] = 0, E [𝜀𝜀𝑖𝑖𝑡𝑡] = 0 [𝜆𝜆𝑖𝑖 + 𝜀𝜀𝑖𝑖𝑡𝑡] = 0. If we

take the first difference of equation (19) as in (20); 𝛥𝛥𝑙𝑙𝑖𝑖𝑡𝑡 = α+ 𝛾𝛾1𝛥𝛥𝑙𝑙𝑛𝑛𝑙𝑙𝑖𝑖𝑡𝑡−1 + 𝛽𝛽′[𝑋𝑋]𝑖𝑖𝑡𝑡 + 𝜆𝜆𝑖𝑖 + 𝛥𝛥𝜀𝜀𝑖𝑖𝑡𝑡 ………………………. (20)

From equation (20), lagged dependent variable 𝛥𝛥𝑙𝑙𝑖𝑖𝑡𝑡 correlates with the error term 𝛥𝛥𝜀𝜀𝑖𝑖𝑡𝑡, this

implies that there is a potential endogenous problem that may render parameter estimates from

equation (20) not consistent, as such, instrument cannot sufficiently be used to address potential

issues in the model. Therefore, a system GMM becomes the only option to address the potential

endogeneity problem in the equation. Following the first difference estimation in equation (20)

above, the following moment of the dynamic GMM can be developed;

E[𝑙𝑙𝑖𝑖𝑡𝑡−𝑠𝑠(𝜀𝜀𝑖𝑖𝑔𝑔 − 𝜀𝜀𝑖𝑖𝑔𝑔−1)] = 0; for t =4, ……….T, s ≥ 3, ………………………. (21)

E[𝑋𝑋𝑖𝑖𝑡𝑡−𝑠𝑠(𝜀𝜀𝑖𝑖𝑔𝑔 − 𝜀𝜀𝑖𝑖𝑔𝑔−1)] = 0; for t =4, ……….T, s ≥ 3, ………………………. (22)

The above equation (21) and (22) can be summarized in the matrix form.

M = ⎣⎢⎢⎢⎡𝑙𝑙𝑖𝑖1 0 0 … … . 0 … . . 0

0 𝑙𝑙𝑖𝑖1 𝑙𝑙𝑖𝑖1 … … 0 … . . 0

. . . . . . .

. . . . . . .

0 0 0 … … 𝑙𝑙𝑖𝑖1 … . . 𝑙𝑙𝑖𝑖,𝑇𝑇−2⎦⎥⎥⎥⎤

M = is the matrix corresponding to the endogenous variables.

13

4. Result and Discussion

The study started by conducting a correlation matrix as presented in table 1. Variables remain

as defined earlier.

Table 1: Correlation Matrix

Variables GDP K L A H TO DD LP

GDP 1

K 0.687*** 1

L 0.616*** 0.481*** 1

A 0.275*** 0.290*** -0.0552 1

H 0.3897** 0.0858* -0.164*** 0.365*** 1

TO -0.287*** -0.270*** -0.181*** -0.106** -0.0339 1

DD 0.347*** 0.0605 -0.196*** 0.564*** 0.408*** -0.112*** 1

LP 0.128*** 0.00185 -0.0661 0.268*** 0.308*** 0.00613 0.443*** 1

Note: Significance is indicated as follows: ***, ** and * for 1%, 5% and 10% respectively.

The correlation matrix was conducted to ensure that the analysis variables do not exhibit near-

perfect correlations among each other. A situation where changes in one of the explanatory

variables can influence the changes in another variable leads to a situation of bias estimate. As

seen, there is no evidence of multicollinearity in the series.

Having established that our model is free from multicollinearity, we proceed to estimate the

panel unit root test using the first-generation approach. The study employed both the Fisher-

based unit root test and Im, Pesaran & Shin (IPS) to check for stationarity because of their

superiority to other first-generation tests.

Variables IPS @ Level IPS @ 1st Difference

Statistics/P-value

Fisher @ Level Fisher @ First

Difference

Fffgg Statistics/P-value Statistic/P-value Statistics/ P-value

LGDP/Lny 4.5457 (1.0000) -12.2639 (0.0000)*** -3.2752 (0.9995) -16.9932 (0.0000)***

LnK 7.8551 (1.0000) -5.3780 (0.0000)*** -4.9545 (1.0000) -6.0923 (0.0000)***

LnL 3.2121 (0.99993) -9.4363 (0.0000)*** -1.7284 (0.958) -13.0225 (0.0000)***

LnH 4.5287 (1.0000) -3.0082 (0.0000)*** -1.1205 (0.8688) -5.3467 (0.0000)***

LnA 2.3452 (1.0000) -6.5636 (0.0000)*** 0.0713 (0.4716) -13.5987 (0.0000)***

LnTO -1.5944(0.0554)** -13.8831 (0.0000)*** -2.0222 (0.0216)*** -18.9747 (0.0000)***

LnDD 3.4453 (0.9995) -3.4982 (0.0000)*** -3.1757 (0.0009)*** -23.8688 (0.0000)***

14

Table 2: Panel Unit Root test Using IPS and Fisher Approach/ AIC Criteria

Notes: The P-value is enclosed in the parentheses. All variables are logged and significance is

indicated as follows: ***, ** and * for 1%, 5%, and 10%, respectively.

We could see from the panel unit root test in table 2 that none of the model's key variables is

stationary at level in both IPS and Fisher-based approach except for the institutional variables.

Of course, judging by the fact that our model's time dimension is relatively small with N > T

and the data are strongly balanced unit root should not be an issue for the study. However, to

ensure there is no room for any doubt on our estimated parameters, the study proceeded to

further differentiate the variables following the suggestion of Bai & Ng (2004) and Moon &

Perron (2004).

The study employed the Westerlund co-integration test to check for the existence of long-run

relationship.

Table 3: Westerlund Co-integration test

Results for H0: no co-integration: With 40 series and 1 covariate

Statistics Value Z-value P-value

Gt -3.442 -11.715 0.0000

Ga -13.465 -7.346 0.0000

Pt -21.952 -12.871 0.0000

Pa -15.912 -16.642 0.0000

From the Westerlund result presented in table 4.3 above, it is evident that all the series

categories from Gt to Pa are significant at 1% level of significance. This implies that null

hypothesis of no co-integration is rejected.

Having validated that there is a long-run relationship between the variables of interest, the

study, therefore, estimated the relationship between the variables using the General Method of

Moment (GMM). Following Roodman (2009) argument, it is important to choose between

system GMM and difference GMM on certain statistics. Following Bond et al. (2001) rule of

thumb approach, it can be revealed that the difference GMM coefficient is close and less than

the fixed effect coefficient, which indicates a negative downward bias of the difference GMM

LnLP -3.1631(0.0008)*** -21.9424 (0.0000)*** -5.5125 (0.0000)*** -37.323 (0.0000)***

15

due to weak instruments as seen in table 4, thereby leaving us with system GMM as the best

estimation technique.

Table 4: Decision Making Criteria

Pooled

OLS

Fixed

Effect

Difference

GMM

System

GMM

Lny_1 -.001828 -0.901180 -0.884942 -0.88063

Remark 1.82% 90.1% 88.4% 88.0%

Source: Author computation from Stata output

The estimate for the three key model is as presented in table 5.

Table 5: System GMM result

Notes: The P-value is enclosed in the parentheses. All variables are logged and significance is

indicated as follows: ***, ** and * for 1%, 5% and 10% respectively.

Source: Author computation from Stata output

As seen in Table 5, when the model was estimated using fixed effect and without accounting

for social capabilities, only two variables labour and capital is significant at 5 percent level of

significance judging by the p-value. Both human capital at difference and level is only

significant at 10 percent with the expected sign. However, when the model were estimated with

Variables Fixed Effect

(Model 1) System GMM

(Model 2) Coeff./P-

value

System GMM/

(Model 3)

System GMM/

(Model 4)

Coeff./P-value Coeff./P-value Coeff./P-value

Lgdp_1 -0.9012(0.000)*** -0.8806 (0.000)*** -0.8962 (0.000)*** -0.8968 (0.000)*** 𝛥𝛥Lk 0.4330(0.000)*** 0.3935 (0.000)*** 0.4073 (0.000)*** 0.4121 (0.000)*** 𝛥𝛥LL 0.5873 (0.000)*** 0.6100 (0.000)*** 0.6456 (0.000)*** 0.7179 (0.001)*** 𝛥𝛥LA 0.2691 (0.272) 0.3322 (0.085)* 0.1575 (0.057)** 1.3804 (0.002)*** 𝛥𝛥LH 0.6486 (0.065)* 0.6203 (0.056)* 0.4437 (0.051)** 0.9416 (0.000)***

LLH 0.6586 (0.057)* 0.6403 (0.051)** 0.7437 (0.000)*** 0.9416 (0.000)***

LTO -0.0459 (0.884)** 0.0228 (0.017)***

LDD 0.0253 (0.027)** 0.0484 (0.0107)***

LLP 0.0009 (0.0957)* 0.0215 (0. 064)*

LH*TO 0.0285 (0.002)***

LH*DD 0.0111 (0.006)***

LH*LP 0.0423 (0.001)**

Observations 880 880 880 880

Number of

c_id

40 40 40 40

AR(2) 0.978 0.799 0.882

Hansen test 0.153 0.148 0.116

F-stat; P-

value (0.000)*** (0.000)*** (0.000)*** (0.000)***

16

GMM, human capital at level became significant though, human capital at difference and

knowledge are both insignificant at 5 percent. Specifically, it was discovered that a 1 percent

rise in the human capital development index across countries will lead to an increase in income

per capita by at least 64.03 percent at 5 percent level of significance. Other variables are also

significant with an expected sign except for knowledge and human capital at difference that

only became significant at 10 percent. The findings also reveal that the popular Solow

conditional convergence holds as the lag endogenous variable has a negative sign and is

consistent with previous studies like Mankiw et al. (1992) and that of Sunde & Vischer (2015).

It was discovered also that when we introduced social capabilities in the model, the impact of

human capital on the growth rate across countries improved by at least 10.33 percent. Similarly,

other variables in the model including labour, capital, and knowledge all witnessed an

improved impact on the difference in cross-country growth rate in per capita income. For

instance, labour increased by at least 3 percent, capital by 1 percent, and human capital by 10

percent. However, the introduction of the social capabilities did not change the Solow

conditional convergence but rather reinforce its impact.

According to Sunde & Vischer (2015), Solow conditional convergence states that, even if

countries differ in their saving rates, population growth rates, and production function (due to

unequal access to technology) they will converge to a steady-state with different capital-labour

ratio and different standards of living in the long-run. In a last-ditch, the study further interacts

human capital with social capabilities, as expected all the interactive variables positively

impact the growth rate of per capita income across country. And the impact of human capital

on economic growth became even stronger with the interaction of social capabilities. For

instance, the introduction of social capabilities in the model increases human capital's impact

on income per capita by 20.13 percent from the initial impact when social capabilities have not

been introduced in the model. The result is expected as an improved democratic system where

laws and policy are adhered to and the existence of checks and balances among the alms of

government individuals rights – political, economic, and property are resected thereby

improving the human capital impact in driving the necessary economic growth. Again,

economic openness offers the citizens a wider market for their products and services, facilitates

technological diffusion in developing countries like Africa.

The f-test p-value equally reveals that all the explanatory variables have a significant

relationship with economic growth across the country since the p-value (0.0000) is much less

17

than a 1 percent level of significance. Looking at the Arellano-Bond test of higher-order serial

correlation in Table 4.6, the AR2 p-value is 0.978, which is much higher than the 10 percent

level of significance as such we cannot reject the null hypothesis of serial correlation. We,

therefore, conclude that the model is free from serial autocorrelation and is fit for analysis.

Also, the model is checked for over-identification and validity of instruments using Hansen-

Sargan test. As seen in Table 4.6 above, the probability value of the Hansen validity test for

instrument validity is 0.153, which is greater than 1 percent level of significance, indicating

that the instrument used are valid.

5. Conclusion and Policy Recommendations.

This study has investigated human capital, social capabilities, and economic growth across

countries. The empirical findings revealed that human capital has a significant impact on the

growth rate of income per capita across countries. We discovered that without accounting for

social capabilities the impact of human capital on growth though positive is weakly significant.

But accounting for social capabilities rekindles the impact of human capital in driving the

growth rate across nations.

The finding is not surprising giving the fact that when the labour force has access to a working

legal system that respects individuals’ rights and freedom and increased economic opportunity,

they will intend to invest more in themselves and their future (human capacity building). An

improved democratic system of government and respect for the rule of law will lead to an

improved educational system, better job opportunities that will instill the hard work spirit and

working institution will decrease the informality in a country as argued by Tonuchi et al (2020).

Therefore, this study concludes that investment in human capital should be a deliberate

decision like the investment in physical capital if the nation intends to grow. And that

investment in human capital will not yield the required result if a sound legal, economic, and

political institution is not deliberately built.

Therefore, the study recommends strong institutional building by investing in the rule of law

and liberty of the citizens and investing in the infrastructural building to ensure a friendly

business environment. It is important to note that infrastructural building improves the

institutional factors thereby improving the relationship between human capital and economic

growth. Building an institution that guarantees everyone's rights and equitable distribution of

income should be the priority of developing countries' leaders. This can be achieved first

18

through a strong check and balances in the three alms of government and easing regulations

that hinder business success in the region.

Competing Interest

Authors declare no competing interests.

Disclaimer

The opinion shared are that of the author and not any institution.

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